# Sand is dumped such that the shape of the sandpile

Asked by wiki @ in Mathematics viewed by 265 People

5. Sand is dumped off a conveyor belt into a pile at the rate of 2 cubic feet per minute. The sand pile is shaped like a cone whose height and base diameter are always equal. At what rate is the height of the pile growing when the pile is 5 feet high? (The volume of a cone is fr2h where r is the radius of the base and h is the height:)​

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

1. Brackets
2. Parenthesis
3. Exponents
4. Multiplication
5. Division
7. Subtraction
• Left to Right

Equality Properties

• Multiplication Property of Equality
• Division Property of Equality
• Subtract Property of Equality

Geometry

Volume of a Cone:

• h is height

Diameter: d = 2r

Calculus

Derivatives

Derivative Notation

Differentiating with respect to time

Basic Power Rule:

• f(x) = cxⁿ
• f’(x) = c·nxⁿ⁻¹

Step-by-step explanation:

Step 1: Define

Step 2: Rewrite Volume Formula

We need to rewrite the cone volume formula in terms of height h only.

Base b = diameter d of the circular base

1. Define:                    b = d
2. Substitute:              b = 2r

We are given that the base of the cone is the same as the height.

1. Define:                    b = 2r
2. Substitute:              h = 2r

Now solve for height.

1. Divide 2 on both sides:                    h/2 = r
2. Rewrite expression:                          r = h/2

Now find new volume formula.

1. Define [VC]:
2. Substitute:
3. Exponents:
4. Multiply:

We now have the same volume formula in terms of height h only.

Step 3: Differentiate

1. Basic Power Rule:
2. Simplify:

Step 4: Solve for height rate

1. Substitute:
2. Isolate h rate:
3. Exponents:
4. Multiply:
5. Divide:
6. Rewrite:

Here this tells us that the rate at which the height is moving at a rate of 0.101859 feet per minute.

## In what sections of a website are manuals commonly found

Asked by wiki @ in SAT viewed by 239 persons

In what sections of a website are manuals commonly found?

## How many calories do you burn jogging for 45 minutes

Asked by wiki @ in Mathematics viewed by 233 persons

Jogging burns 375 calories in 45 minutes. determine how many calories are burned per hour

## What is the climate of the selva in south america

Asked by wiki @ in Geography viewed by 225 persons

What is the climate of the selva in south america?

## Identify and calculate the area and perimeter for each quadrilateral

Asked by wiki @ in Mathematics viewed by 204 persons

Identify and calculate the area and perimeter for this polygon.

## 0.075 m to cm

Asked by wiki @ in Chemistry viewed by 102 persons

Make the following conversion. 0.075 m = _____ cm 7.5 75 0.0075 0.00075

## 9 6 factoring trinomials of the type ax2 bx c

Asked by wiki @ in Mathematics viewed by 183 persons

The method used to factor trinomials of the form ax^2+bx+c can also be used to factor binomials of the form px^2+q by realizing that, in this case, _____. A. a …

## How do you find the parent function of a graph

Asked by wiki @ in Mathematics viewed by 247 persons

Name a parent function where the graph is shaped like the letter "u". Name a parent function where the graph is shaped like the letter "v"?

## How was the british parliament reformed during the early 1800s

Asked by wiki @ in History viewed by 161 persons

How was the british parliament reformed during the early 1800s.?

## How to find the rate of change of a table

Asked by wiki @ in Mathematics viewed by 263 persons

How can you find the rate of change from a table?

## Where is over 95 of incoming ultraviolet radiation absorbed

Asked by wiki @ in Physics viewed by 182 persons

Where is over 95% of incoming ultraviolet radiation absorbed?. a.. the stratosphere. b.. the mesosphere. c.. the troposphere. d.. the thermosphere. .

## What does the green light symbolize in the great gatsby

Asked by wiki @ in English viewed by 289 persons

What does the green light mostly symbolize in the Great Gatsby

## Why did the us decide to bomb hiroshima and nagasaki

Asked by wiki @ in History viewed by 280 persons

Why did Truman decide to drop the atomic bomb on Hiroshima?

## What two groups are the primary focus in market research

Asked by wiki @ in Biology viewed by 223 persons

What two groups are the primary focus in market research

## Energy is conserved this means that in any system _____

Asked by wiki @ in Physics viewed by 194 persons

Energy is conserved. this means that in any system, _____.

## A favorable balance of trade occurs when the value of

A favorable balance of trade occurs when the value of

## How many square feet does 1 bag of mulch cover

Asked by wiki @ in Mathematics viewed by 255 persons

Nicholas is covering a triangular area with mulch. The base of the area is 22 feet, and the height is 10 feet. One bag of mulch covers 8 square feet. …

## What is one reason dante most likely wrote the inferno

Asked by wiki @ in English viewed by 217 persons

What is one reason Dante most likely wrote the Inferno? A: to fight against the church's view of hell B: to pass judgement on important religious leaders C: to gain …

## How to know if a table is a linear function

Asked by wiki @ in Mathematics viewed by 361 persons

Which table represents a linear function?

## The amount of energy or fuel in food is called

Asked by wiki @ in Health viewed by 382 persons

The amount of energy or fuel in food is called ____________.

## How many decibels of noise can cause temporary hearing loss

Asked by wiki @ in Health viewed by 205 persons

How many decibels of noise can cause temporarily hearing lose?

## What was one result of the second great awakening edgenuity

Asked by wiki @ in History viewed by 128 persons

What was one result of the second great awakening? A. Religion remain separate from social issues B. Reform movement developed and took hold C. The Quakers were condemned for their …

## Name 7 characteristics that can be used to describe minerals

Asked by wiki @ in English viewed by 255 persons

Name seven characteristics that can be used to describe minerals

## Group contains elements like fluorine chlorine bromine iodine and astatine

Asked by wiki @ in Physics viewed by 196 persons

Group__ contains elements like fluorine chlorine bromine iodine and astatine

Which best describes the Business, Management, and Administration career cluster? These are careers that are focused on running businesses. These are careers that combine medical services, coding, and sales. These …

## Which of the following is not a barrier to entry

Which of the following is NOT a barrier to entry that would allow a monopolist to keep potential competitors out of its market? Significant economies of scale exist. The firm …

## Matter is neither created nor destroyed in a chemical reaction

Asked by wiki @ in Chemistry viewed by 171 persons

The statement, "In a chemical reaction, matter is neither created nor destroyed" is called a the Law of Multiple Proportions. b Dalton's Atomic Theory. c the Law of Definite Proportions. …

## Why are ions charged particles and thus no longer neutral

Asked by wiki @ in Chemistry viewed by 196 persons

Forming ionic bonds 1. a chemical bond that forms when electrons are transferred from one atom to another is a(n) 2. charged particles that form when atoms gain or lose …

## Que se celebra el 4 de julio en puerto rico

Asked by wiki @ in Spanish viewed by 270 persons

El dia de la independencia de puerto rico es el 4 de julio o el 23 de septiembre.

## What is the purpose of a signal phrase

Asked by wiki @ in English viewed by 112 persons

What is the purpose of a signal phrase?

## How have biology and philosophy shaped the development of psychology

Asked by wiki @ in Social Studies viewed by 162 persons

How have biology and philosophy shaped the development of psychology?

## Gina wilson all things algebra 2015 answer key unit 11

Asked by wiki @ in Mathematics viewed by 5677 persons

## Unit 11 volume and surface area homework 3 answer key

Asked by wiki @ in Mathematics viewed by 4896 persons

## 3.2 puzzle time what is roz savage famous for answers

Asked by wiki @ in Mathematics viewed by 3881 persons

## What did captain hook say in the bakery worksheet answers

Asked by wiki @ in Mathematics viewed by 3750 persons

## An artist sells a painting for 20.50 but uses 5.75

Asked by wiki @ in Mathematics viewed by 3404 persons

## Gina wilson all things algebra 2016 answer key unit 11

Asked by wiki @ in Mathematics viewed by 3118 persons

## Unit 4 congruent triangles homework 1 classifying triangles gina wilson

Asked by wiki @ in Mathematics viewed by 2961 persons

## Why did the picture go to jail puzzle time answers

Asked by wiki @ in Mathematics viewed by 2948 persons

## Geometry unit 11 volume and surface area quiz 11 1

Asked by wiki @ in Mathematics viewed by 2925 persons

## Unit 1 test study guide geometry basics answer key

Asked by wiki @ in Mathematics viewed by 2761 persons

## Cryptic quiz what is the opposite of a professional eater

Asked by wiki @ in Mathematics viewed by 2620 persons

## The price of salmon at a fish market is 5.40

Asked by wiki @ in Mathematics viewed by 2588 persons